Problem: $A$ $B$ $C$ If: $ AB = 5x + 5$, $ AC = 64$, and $ BC = 2x + 3$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {5x + 5} + {2x + 3} = {64}$ Combine like terms: $ 7x + 8 = {64}$ Subtract $8$ from both sides: $ 7x = 56$ Divide both sides by $7$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $BC$ $ BC = 2({8}) + 3$ Simplify: $ {BC = 16 + 3}$ Simplify to find ${BC}$ : $ {BC = 19}$